Posted by **mr maths** on Friday, January 1, 2010 at 7:45pm.

find the gradient of the tangent to the parabola y=4x-x^2 at (0,0)

hence calculate the size of the angle between the line y=x and this tangent.

(as i cant show you the diagram all that it shows is the line going through (0,0) and having one point of contact)

- maths -
**Reiny**, Friday, January 1, 2010 at 8:05pm
This is a Calculus question.

dy/dx = 4 - 2x

at (0,) dy/dx = 4

so the slope or gradient of the tangent at (0,0) is 4

and the slope of y = x is 1

Did you know that the slope of a line is the same as the tangent of the angle that line makes with the x-axis?

so the line with slope of 4 makes an angle of 75.96º with the x-axis

the line y=x makes and angle of 45º with the x-axis

so the angle between them is (75.96-45)º

= 30.96º

## Answer This Question

## Related Questions

- Calculus - Maths - I got a few questions. Hope ya'll can help out. 1) for F(X...
- Maths - I need some help with my maths questions please! What angle does the ...
- math - Draw a diagram to show that there are two tangent lines to the parabola y...
- Calc. - Find the area of the region bounded by the parabola y=x^2, the tangent ...
- Maths - In an orthonormal system, you're given the following: Point P(1,2) Lina ...
- Math - If f(x)=3x^2-5x, find the f'(2) & use it to find an equation of tangent ...
- Calculus AB - Could someone please help me with these tangent line problems? 1) ...
- Calculus - Draw a diagram to show that there are two tangent lines to the ...
- Mathematics - In an orthonormal system, you're given the following: Point P(1,2...
- maths - consider the line y=6x-k and the parabola y=x^2 i) for what value of k ...

More Related Questions